Probabilistic Burnside groups

Gil Goffer; Be'eri Greenfeld

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arXiv · 2306.11204

Probabilistic Burnside groups

Gil Goffer·Be'eri Greenfeld

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Abstract

We prove that there exists a finitely generated group that satisfies a group law with probability 1 but does not satisfy any group law. More precisely, we construct a finitely generated group G in which the probability that a random element chosen uniformly from a finite ball in its Cayley graph, or via any non-degenerate random walk, satisfies the group law x^k=1 for some (fixed) integer k, tends to 1. Yet, G contains a non-abelian free subgroup, and therefore G does not satisfy any group law. In particular, this answers two questions of Amir, Blachar, Gerasimova, and Kozma.

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BibTeX RIS

Gil Goffer, Be'eri Greenfeld. 2023-06-20. Probabilistic Burnside groups. https://arxiv.org/abs/2306.11204

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